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Answer to Question #6241 in Trigonometry for joy

Question #6241
sin(x)^2=2cos(x)+2
Expert's answer
Due to the famous identity cos2x+sin2x=1 therefore sin2x=1-cos2x
So sin2x=1-cos2x =2cos x+2
Let's denote cos x=t. We suppose that -1<=t<=1
So we get the equation:
1-t^2=2t+2
t^2+2t+1=0
(t+1)^2=0
t=-1
So cos x=-1
x=pi+2k pi where k - integer

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